Rigid Body Research Articles

Pushing AFM to the Boundaries: Interphase Mechanical Property Measurements near a Rigid Body

Pushing AFM to the Boundaries: Interphase Mechanical Property Measurements near a Rigid Body

Vehicle Collision Analysis of the Reinforced Concrete Barriers Installed on Bridges Using Node-Independent Model

This paper focuses on improving vehicle collision simulations using finite element analysis (FEA) to examine interactions between reinforced concrete barriers and bridge decks. Three scenarios are explored: treating the barrier as a rigid body, analyzing reinforcement with a fixed base, and including the bridge deck’s cantilever portion beneath the barrier. Except for the rigid body model, a node-independent approach models the complex interactions between reinforcement and concrete in barriers on the bridge deck. This study evaluates barrier strength, occupant risk, and post-collision vehicle safety. Strength is assessed by examining stress in reinforcement and concrete, while occupant risk is measured using Theoretical Head Impact Velocity (THIV) and Post-impact Head Deceleration (PHD). Vehicle trajectory during collisions is also analyzed for stability. The results show significant differences in stress distribution and failure patterns when the bridge deck is considered compared to scenarios without it. Occupant risk evaluations suggest more flexible responses when the bridge deck is included. However, vehicle trajectory post-collision showed no significant differences across scenarios. These findings indicate that modeling efficiency varies based on evaluation criteria, suggesting a more realistic and effective approach for assessing barriers on bridges.

Interaction of complex particles: A framework for the rapid and accurate approximation of pair potentials using neural networks

Motivated by the limitations of conventional coarse-grained molecular dynamics for simulation of large systems of nanoparticles and the challenges in efficiently representing general pair potentials for rigid bodies, we present a method for approximating general rigid body pair potentials based on a specialized type of deep neural network that maintains essential properties, such as conservation of energy and invariance to the chosen origins of the particles. The network uses a specialized geometric abstraction layer to convert the relative coordinates of the rigid bodies to input more suitable to a conventional artificial neural network, which is trained together with the specialized layer. This results in geometric representations of the particles optimized for the specific potential. The network can be trained directly on scalar values to fit a model without explicit gradient and then used to efficiently evaluate the force and torque on the particles resulting from the potential. The concept is demonstrated with an atomistic interaction model for carbon nanotubes and the resulting model is compared with a common type of coarse-grained model optimized for the same potential, with even very small networks comparing favourably and larger networks achieving up to two orders of magnitude lower cost. The sensitivity to noise in the training data is investigated and the model is found to strongly reject noise up to 12.5% given a dataset of 107 samples. The performance of a proof-of-concept implementation is demonstrated on a variety of hardware, showing the models viability for large-scale simulations. Furthermore, generalization to soft bodies and potentials for polydisperse systems are discussed. Published by the American Physical Society 2024

Numerical analysis of the effect of tunnel hydrofoil - stern flap on the motion stability of a double M-craft in regular waves

Abstract The double M-craft is a new type of high-performance multi-hull vessel that combines the gliding characteristics of a planing boat with the resistance-reducing characteristics of a hovercraft. But it also suffers from motion instability in regular waves. At present, there is scarce study on the effect of appendage on the motion stability of double M-craft in regular waves. By using the software STAR-CCM+ to numerically simulate the pitching and heaving motions of a double M-craft installed with tunnel hydrofoils and stern flaps in regular waves. Based on the overset mesh technology, the volume of fluid (VOF) method is used to capture the water-gas two-phase flow field. The 2-degree of freedom (2-DOF) motion of the rigid body is simulated by dynamic fluid body Interaction (DFBI). After investigating the effects of these combined appendages on the hydrodynamic performance, running attitude, and motion response of a double M-craft in regular waves, the optimal mounting parameters of the combined appendage have been obtained. The results have shown that all nine types of combined appendages can reduce the heave and pitch. The optimal combined appendage installation parameters include a hydrofoil longitudinal mounting position of 1/8L, angle of attack of 3°, stern flap length of 1.5%L, and flap angle of 5°, which can effectively reduce the pitching response by about 8% and reduce the swaying response by about 2.6%, and enhance its longitudinal motion stability.

Scalable O(log2n) Dynamics Control for Soft Exoskeletons

Robotic exoskeletons are being actively applied to support the activities of daily living (ADL) for patients with hand motion impairments. In terms of actuation, soft materials and sensors have opened new alternatives to conventional rigid body structures. In this arena, biomimetic soft systems play an important role in modeling and controlling human hand kinematics without the restrictions of rigid mechanical joints while having an entirely deformable body with limitless points of actuation. In this paper, we address the computational limitations of modeling large-scale articulated systems for soft robotic exoskeletons by integrating a parallel algorithm to compute the exoskeleton’s dynamics equations of motion (EoM), achieving a computation with O(log2n) complexity for the highly articulated n degrees of freedom (DoF) running on p processing cores. The proposed parallel algorithm achieves an exponential speedup for n=p=64 DoF while achieving a 0.96 degree of parallelism for n=p=256, which demonstrates the required scalability for controlling highly articulated soft exoskeletons in real time. However, scalability will be bounded by the n=p fraction.

An MPC-DCM Control Method for a Forward-Bending Biped Robot Based on Force and Moment Control

For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots based on linear inverted pendulum, and Model Predictive Control (MPC) is an optimization solution strategy using rolling optimization. In this paper, DCM theory is applied to the state transition matrix of the system, combined with simplified rigid body dynamics, the mathematical description of the biped robot system is established, the classical MPC method is used to optimize the control input, and DCM constraints are added to the constraints of MPC, making the real-time DCM approximate to a straight line in the walking single gait. At the same time, the linear angle and friction cone constraints are considered to enhance the stability of the robot during walking. In this paper, MATLAB/Simulink is used to simulate the robot. Under the control of this algorithm, the robot can reach a walking speed of 0.75 m/s and has a certain anti-disturbance ability and ground adaptability. In this paper, the Model-H16 robot is used to deploy the physical algorithm, and the linear walking and obstacle walking of the physical robot are realized.

SEC-SAXS/MC Ensemble Structural Studies of the Microtubule Binding Protein Cdt1 Show Monomeric, Folded-Over Conformations.

Cdt1 is a mixed folded protein critical for DNA replication licensing and it also has a "moonlighting" role at the kinetochore via direct binding to microtubules and the Ndc80 complex. However, it is unknown how the structure and conformations of Cdt1 could allow it to participate in these multiple, unique sets of protein complexes. While robust methods exist to study entirely folded or unfolded proteins, structure-function studies of combined, mixed folded/disordered proteins remain challenging. In this work, we employ orthogonal biophysical and computational techniques to provide structural characterization of mitosis-competent human Cdt1. Thermal stability analyses shows that both folded winged helix domains1 are unstable. CD and NMR show that the N-terminal and linker regions are intrinsically disordered. DLS shows that Cdt1 is monomeric and polydisperse, while SEC-MALS confirms that it is monomeric at high concentrations, but without any apparent inter-molecular self-association. SEC-SAXS enabled computational modeling of the protein structures. Using the program SASSIE, we performed rigid body Monte Carlo simulations to generate a conformational ensemble of structures. We observe that neither fully extended nor extremely compact Cdt1 conformations are consistent with SAXS. The best-fit models have the N-terminal and linker disordered regions extended into the solution and the two folded domains close to each other in apparent "folded over" conformations. We hypothesize the best-fit Cdt1 conformations could be consistent with a function as a scaffold protein that may be sterically blocked without binding partners. Our study also provides a template for combining experimental and computational techniques to study mixed-folded proteins.

Development of a Large-Aperture Coordinate Precision Measurement Instrument Using Differential Geometric Error Weighting

The accuracy of traditional measuring machines is affected by the measuring range and sensitive geometric errors, and it is not possible to combine large caliber and high-precision measurements. This study proposes a differential geometric error-weighting method for designing a high-precision, large-diameter measuring machine. The machine utilized a zero-Abbe arm structure and applied the rigid body theory and small-angle hypothesis to model geometric errors. Weights were calculated for 23 geometric errors, identifying eight sensitive ones. A picometer-precision laser interferometer (quDIS) with a theoretical positioning accuracy of 0.2 nm/mm and standard flat rulers are used to ensure highly accurate positioning of the Y-axis/Z-axis of the measuring platform and reduce the straightness of both axes by approximately 75%, with radial and axial runout of the rotary table under 100 nm. The development and design method of the high-precision measuring machine proposed in this study is applicable to large-diameter high-precision flexible measurement, and the accurate control of measuring machine movement accuracy is realized by calculating the geometric error weights.

Stochastic dissipative Euler’s equations for a free body

Abstract Intrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler’s equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler’s equations in a thermodynamically consistent way (European Journal of Mechanics – A/Solids 103, 105,184 (2024)). This framework describes the evolution of both orientation and shape of a free body, incorporating internal thermal fluctuations and their concomitant dissipative mechanisms. In the present work, we demonstrate that, in the absence of angular momentum, the theory predicts that the principal axes unit vectors of a body undergo an anisotropic Brownian motion on the unit sphere, with the anisotropy arising from the body’s varying moments of inertia. The resulting equilibrium time correlation function of the principal eigenvectors decays exponentially. This theoretical prediction is confirmed in molecular dynamics simulations of small bodies. The comparison of theory and equilibrium MD simulations allow us to measure the orientational diffusion tensor. We then use this information in the Stochastic Dissipative Euler’s Equations, to describe a non-equilibrium situation of a body spinning around the unstable intermediate axis. The agreement between theory and simulations is excellent, offering a validation of the theoretical framework.

Exergetic port-Hamiltonian systems for multibody dynamics

AbstractMultibody dynamics simulation plays an important role in various fields, including mechanical engineering, robotics, and biomechanics. Setting up computational models however becomes increasingly challenging as systems grow in size and complexity. Especially the consistent combination of models across different physical domains still requires significant effort. This motivates the study of formal languages that enable a compositional approach to modeling multiphysical systems with basic guarantees. The paper shows how multibody systems, or more precisely assemblies of rigid bodies connected by lower kinematic pairs, can be described as Exergetic Port-Hamiltonian Systems (EPHS). The EPHS modeling language features a straightforward graphical syntax for expressing the energy-based interconnection of hierarchically nested subsystems. This reduces cognitive load and facilitates clearer communication among experts, nonexperts, and computational tools. Hierarchical nesting of systems enables abstraction of lower-level details and promotes the reuse of models at different levels of complexity. At the lowest level, there are three basic kinds of systems, representing energy storage and reversible/irreversible energy exchange. The structured approach guarantees fundamental properties of macroscopic systems, such as conservation of energy and nonnegative entropy production. In combination with the compositional syntax, this makes building and modifying models simpler and less error-prone.

Optomechanical motions of gold dimer’s spin, rotation and revolution manipulated by bessel beam

The optomechanical motion of a gold nanoparticle (GNP) dimer—a pair of optically bound GNPs—in fluid, manipulated by a Bessel beam, is theoretically studied using the multiple multipole (MMP) method. Since a Bessel beam possesses orbital angular momentum (OAM) and spin angular momentum (SAM) simultaneously, complicated rigid-body motions of the dimer can be induced. The mechanism involves the equilibrium between the optical force with the reactive drag force exerted by the fluid. Our results demonstrate that the dimer rotates around its center of mass (COM), while the COM performs an orbital revolution around the optical axis. Additionally, each individual GNP undergoes spinning. The directions of the GNPs’ spin and the orbital revolution of COM depend on the handedness and the order (topological charge) of Bessel beam, respectively. Nevertheless, the rotation direction of the dimer depends on the size of GNP. In the case of a smaller dimer, the direction of dimer’s rotation with respect to the COM is consistent with the handedness of the light. Conversely, a larger dimer performs a reverse rotation, accompanied by a precession during the orbital revolution. There are multiple turning points in the radius of the GNP for the alternating rotation of the dimer caused by positive or negative optical torque. Our finding may provide an insight to the optomechanical manipulation of optical vortexes on the motions of GNP clusters.

Ship-shaped vessel hydroelastic numerically supported analysis in a narrow ultra-reduced model tank with full scale extrapolation

Although the rigid body hypothesis is broadly used when studying floating bodies dynamics, it is known that a ship-shaped vessel will have hydroelastic responses. Considering a conventional closed main deck hull in which the ship's length is considerably greater than its breadth, it is expected that the vertical bending moments can represent an important load that must be considered to guarantee structural integrity. Numerical models can be developed to assess the hydroelastic response, but the validation process is necessary. Model tests can be performed to validate the numerical model and require specific considerations to properly represent hydroelastic phenomena, such as having equivalent bending stiffness when compared to the full-scale body. Many experimental facilities that can be used to perform such experiments consist of narrow wave channels, in which the wall effect will influence the model's dynamics. This work implements a Tank Green Function (TGF) to a numerical model developed in Capytaine to represent the wall effect on the body's response. The numerical results were then compared to experimental data from tests in a narrow wave channel and good adherence was found. The validated numerical model can then be used to simulate open-water conditions, so the results can be extrapolated to full scale without the need to perform model tests in an ocean tank in which the wall effect would not be relevant.

Analytical assessment of suspension bridge's 3D curved cable configuration and cable clamp pre-installation angle considering the main cable torsional and flexural stiffnesses

For a suspension bridge with a spatial cable system, the 3D curved main cable undergoes large lateral and torsional deformations during construction, which increases the difficulty of construction control. If using the traditional ideal flexible cable assumption, the torsional deformation cannot be analyzed. Therefore, incorporating the main cable's torsional and flexural stiffnesses in shape-finding analysis remains highly challenging. This study develops an analytical method for determining the target configuration of the main cable by applying the multi-segment catenary method and the Cosserat rod model. The closed-form solution of the geometrically exact force-displacement-strain relationships is derived, comprehensively considering the tension, shear, bending, and torsion of the main cable, as well as the initial curvatures and axial strains in the reference configuration. Then a two-layer shape-finding framework is established, with the first layer being recursive calculations of the cable shape and the second layer being numerical calculations of the nonlinear governing equations using the Levenberg-Marquardt method. Furthermore, a novel method for calculating the pre-deflection angle of the cable clamp in the free cable state is presented for the first time. A classic cantilever model and a suspension bridge with the spatial main cable are studied to investigate the accuracy of the proposed algorithms. Numerical results indicate that when the spatial main cable is twisted, the bottom edge of the cable cross-section moves outward along the transverse direction of the bridge. The torsion of the main cable includes both elastic deformation and rigid body displacement caused by the bidirectional bending effect. At the mid-span, the torsional angle of the main cable cross-section is 10.088°, and the pre-deflection angle of the cable clamp at the mid-span should be set to 10.851°. Moreover, the target configuration is highly sensitive to the flexural and torsional stiffnesses of the main cable while the effect of shear deformations on cable configurations can be ignored.

Uncertainty analysis of hypersonic flight dynamics under elastic effects

Abstract In addressing the aerodynamic-elastic coupling issues of hypersonic vehicles, this study delves into the analysis of the elastic deformation of the aircraft based on mechanistic understanding. It employs the Interval Analysis Method based on Polynomial Approximations to conduct uncertainty analysis of the aerodynamic model under elasticity, delineating the range of uncertainty in the aerodynamic model influenced by elastic deformation. The aerodynamic force of the aircraft under elasticity is connected with the rigid body, and then the aerodynamic layout of the aircraft fuselage and control surface after elastic deformation is calculated to study the influence of the elastic effect on the aerodynamic force. The results show that the change caused by uncertainty has a relatively small effect on lift but a relatively large effect on drag and pitching moment.

On space–time diversity in shock train self-excited oscillation mode during wide-range evolution in a scramjet isolator

The shock train self-excited oscillation can induce combustor instabilities and reduce engine margin. In a dual-mode scramjet, the shock train undergoes a complete evolution process, exhibiting structural changes closely tied to this inherent unsteadiness. This study aims to elucidate the space–time diversity in shock train self-excited oscillation mode and the underlying mechanisms during wide-range evolution. The experimental investigations were conducted at Ma = 1.95, capturing the complete evolution of the shock train. The results indicate the evolution can be categorized into three regimes based on structural characteristics. In regime I, the shock region gradually forms, followed by the occurrence of the mixing region in regime II. Regime III corresponds to inlet unstart. In regime II, isolator outlet pressure fluctuations exhibit higher frequency and lower amplitude compared to regime I, while the shock motion demonstrates lower frequency and higher amplitude. The shock train behaves in a large-scale, low-frequency (1.53 times the duct height, 10 Hz) unsteady motion in regime II, posing a potential threat to engine operation. Coherence and phase analysis reveal the disturbance source originates downstream. Proper orthogonal decomposition modal analysis shows two oscillation modes: low-frequency components correspond to shock motion, and high-frequency components correspond to pressure fluctuations across the entire pseudoshock. The propagating of downstream disturbance differs between the two regimes. In regime I, the shock train exhibits rigid-body motion synchronously. In regime II, the relative motion between each shock wave and the cumulative effect of pressure disturbance lead to frequency decay upstream, amplifying the shock train motion.

Effect of geometric variations on the wing rock of blended wing-body aircraft

Blended wing-body configurations are anticipated to dominate future transport and military aerospace designs. The departure of the conventional tube-wing configuration has opened several areas of investigation. These designs are susceptible to lateral instability during landing, takeoff, and maneuvering flight despite having improved aerodynamics because of their tailless nature. One of these instabilities, Wing-Rock, poses significant performance and operational difficulties and can potentially cause crashes. Though experimental and numerical studies of the aerodynamics and stability of blended wing-body configurations have been conducted, wing-rock characteristics still need to be identified in the literature. This research aims to investigate these characteristics at low subsonic speeds with varying outboard sweep and geometric twist angles. The study includes a numerical approach based on the rigid body free-vibration method in single roll degree of motion, which uses three-dimensional unsteady Reynolds’ Average Navier Stokes equations, and an analytical approach based on the multiple time scale method, which captures the crucial aspect of the wing rock system. The findings show that the geometrical parameters significantly impact the wing rock characteristics, which are unique to such novel tailless designs.

Neutron tomography and image registration methods to study local physical deformations and attenuation variations in treated archaeological iron nail samples

This study presents a preliminary examination of the effects of environment changes post-excavation on heavily corroded archaeological Roman iron nails using neutron tomography and image registration techniques. Roman nails were exposed to either a high relative humidity environment, or fast thermal drying as primary experiments to show the power of this imaging technique to monitor and quantify the structural changes of corroded metal artifacts. This research employed a series of pre- and post-treatment tomography acquisitions (time-series) complemented by advanced image registration methods. Based on mutual information (MI) metrics, we performed rigid body and affine image registrations to meticulously account for sample repositioning challenges and variations in imaging parameters. Using non-affine local registration results, in a second step, we detected localized expansion and shrinkage in the samples attributable to imposed environmental changes. Specifically, we observed local shrinkage on the nail that was dried, mostly in their Transformed Medium (TM), the outer layer where corrosion products are cementing soil and sand particles. Conversely, the sample subjected to high relative humidity environment exhibited localized expansion, with varying degrees of change across different regions. This work highlights the efficacy of our registration techniques in accommodating manual removal or loss of extraneous material (loosely adhering soil and TM layers around the nails) post-initial tomography, successfully capturing local structural changes with high precision. Using differential analysis on the accurately registered samples we could also detect and volumetrically quantify the variation in moisture and detect changes in active corrosion sites (ACS) in the sample. These preliminary experiments allowed us to advance and optimize the application of a neutron tomography and image registration workflow for future, more advanced experiments such as humidity fluctuations, corrosion removal through micro-blasting, dechlorination and other stabilization treatments.

ANCF-based modelling of rigid-flexible coupling of helicopter flexible rotor blades

Abstract A high-precision rotor structure dynamic model applicable to a variety of helicopter blade hub structures is established considering rotor blade flexible deformation. The absolute nodal coordinate method is applied to the traditional rotor blade rigid-flexible coupling dynamics model, making the new model applicable to both fully articulated rotor blades and other advanced blade hub structures. No small-volume assumptions were made in the modelling process. Both Green’s strain expression under finite deformation and the geometrical relation of elastic deformation motion based on the absolute nodal coordinate method are used to derive the blade strain energy, kinetic energy, and the external load virtual work. The rotation angle at the articulation constraint at the root of the blade coupled with the elastic deformation degrees of freedom of the blade in three independent rigid body degrees of freedom, respectively. The rotor blade rigid-flexible coupling dynamics equations were established according to the Hamilton action principle. The time-domain simulation is carried out under a free single pendulum and fixed rotational speed/fixed torque for the established flexible blade model, which verifies the validity and high accuracy of the rigid-flexible coupling articulation model of the flexible rotor blade and the blade hub.

Unsteady aerodynamic modeling and flight trajectory simulation of dual-spin projectile based on DNN and transfer-learning

To evaluate flight performance and aerodynamic characteristics of a dual-spin projectile, the coupled computational fluid dynamics and rigid body dynamics (CFD/RBD) method is commonly used, which can simultaneously solve the flight mechanics and flow field. However, the efficiency is compromised by the large number of CFD calculations required. This paper develops an unsteady aerodynamic modeling method that combines deep neural networks and transfer learning, which can accurately predict unsteady aerodynamics of dual-spin projectiles under varying initial conditions. Considering the influence of flight state and aerodynamic data from short-term historical moments, we integrate them as input features of the aerodynamic model to reduce the impact of long-term historical data. To enhance the model generalization under varying initial conditions, we fine-tune the built aerodynamic model using small amounts of data under new conditions by transfer learning. The proposed method is validated through interpolated and extrapolated prediction cases, respectively. The results indicate that the proposed method can achieve better accuracy and generalizability than long short-term memory neural networks and autoregressive moving average method in unsteady aerodynamic modeling of the dual-spin projectile. By coupling the flight dynamics equations with the aerodynamic model in the time domain, the flight simulation only takes a few seconds, which can reduce computing time by three orders of magnitude compared to the coupled CFD/RBD method.

Modifications of SPH towards three-dimensional simulations of an icy moon with internal ocean

There are some traces of the existence of internal ocean in some icy moons, such as the vapor plumes of Europa and Enceladus. This implies a region of liquid water beneath the surface ice shell. Since liquid water would be essential for the origin of life, it is important to understand the development of these internal oceans, particularly their temperature distribution and evolution. The balance between tidal heating and radiative cooling is believed to sustain liquid water beneath an icy moon’s surface. We aim to simulate the tidal heating of an internal ocean in an icy moon using 3-dimensional numerical fluid calculations with the Smoothed Particle Hydrodynamics (SPH) method. We incorporated viscosity and thermal conduction terms into the governing equations of SPH. However, we encountered two issues while calculating rigid body rotation using SPH with a viscous term: (1) conventional viscosity formulations generated unphysical forces that hindered rotation, and (2) there was artificial internal energy partitioning within the layered structure, which was due to the standard SPH formulations. To address the first issue, we modified the viscosity formulation. For the second, we adopted Density Independent SPH (DISPH) developed in previous studies to improve behavior at discontinuous surfaces. Additionally, we implemented radiative cooling using an algorithm to define fluid surfaces via the particle method. We also introduced an equation of state accounting for phase transitions. With these modifications, we have refined the SPH method to encompass all necessary physical processes for simulating the evolution of icy moons with internal oceans.